Then you can boot a new virtual machine instance using the uploaded
image ID.

Will the image work on another cloud platform than OpenStack?

If your platform supports the EC2 style metadata server (which is
contacted by cloud-init), and also supports an HDD image (using either
raw or qcow2 format), then most likely it will work. Note that it will
not work on Amazon EC2 if you are not using the HVM mode.

How can I verify my download is correct and exactly what has been
created by Debian?

There are files here (SHA1SUMS, SHA256SUMS, etc.) which contain
checksums of the images. These checksum files are also signed - see
SHA1SUMS.sign, SHA256SUMS.sign, etc. Once you've downloaded an image, you
can check: